1. **State the problem:** Solve the quadratic equation $x^2 + 6x = 25$. 2. **Complete the square:** To solve by completing the square, add the square of half the coefficient of $x$ to both sides. The coefficient of $x$ is 6, half of it is $\frac{6}{2} = 3$, and its square is $3^2 = 9$. So, add 9 to both sides: $$x^2 + 6x + 9 = 25 + 9$$ 3. **Rewrite as a perfect square:** $$ (x + 3)^2 = 34 $$ 4. **Take the square root of both sides:** $$ x + 3 = \pm \sqrt{34} $$ 5. **Solve for $x$:** $$ x = -3 \pm \sqrt{34} $$ So the two solutions are: $$ x = -3 + \sqrt{34} \quad \text{and} \quad x = -3 - \sqrt{34} $$